In the following question, the firm has constant returns to scale. The productio

Question

In the following question, the firm has constant returns to scale. The production function is q = f(k,l) = k^0.25l^0 .75

Suppose the firm gets both a doubling of both capital and labor productivity. Before the change it had a cost of producing 10 units of c(10) = 500. What is c(10) after the change, if prices of labor and capital are unchanged? Explain briefly.

The answer that c(10) will be cut by half. If a firm has decreasing or increasing returns to scale, what equations/how would I figure out the change in c(10)?

Explanation / Answer

let k = 2k and l=2l then the productivity function is

q(new) = 2k^0.252l^0.75 = 2^(0.25+0.75)k^0.25l^0.75 = 2q

So at same cost now firm is able to produce double units i.e. now firm can produce 20 units in 500 so c(10) will be 500/20*10 = 250 now

Let the production function is q=k^al^b

If a firm has decreasing return to scale i.e. if factors are doubled the production will increase less than double so cost will reduce by less than half it happen when a+b<1

If a firm has increasing return to scale i.e. if factors are doubled the production will increase more than double so cost will reduce by more than half it happen when a+b>1

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